“Let’s say Ron Paul is Nirvana,” said Kennedy, the television personality and former MTV host, by way of explaining the sort of politician who excites libertarians like herself. “Like, the coolest, most amazing thing to come along in years, and the songs are nebulous but somehow meaningful, and the lead singer kills himself to preserve the band’s legacy.

“Then Rand Paul — he’s Pearl Jam. Comes from the same place, the songs are really catchy, can really pack the stadiums, though it’s not quite Nirvana.

“Ted Cruz? He’s Stone Temple Pilots. Tries really hard to sound like Pearl Jam, never gonna sound like Nirvana. Really good voice, great staying power — but the whole is not greater than the sum of its parts.”

I met Kennedy (a gabby 41-year-old whose actual name is Lisa Kennedy Montgomery) in Midtown Manhattan at Fox News headquarters, where she hosts a Fox Business Network program called “The Independents.” By cable TV standards, the show, which is shown four times a week, is jarringly nonpartisan, for the simple reason that she and her co-hosts — the Reason magazine editor in chief Matt Welch and the entrepreneur Kmele Foster — are openly contemptuous of both parties. Kennedy spent most of the Bill Clinton ‘90s as MTV’s most vocal Republican, but then she soured on the G.O.P., a political shift that solidified during the spending and warring and moralizing excesses of the George W. Bush years. Sometime after the elephant tattoo on her left hip “got infected and started looking more like a pig,” Kennedy began thinking of herself as a libertarian instead. She, Welch and Foster take turns on the show bashing not only “Obamacare” but also the N.S.A., neoconservatives and social scolds. It’s not a hospitable forum for G.O.P. talking points. “There are some libertarian-leaning Republicans who are afraid to be on our show,” Kennedy told me. Libertarianism’s Nirvana, a k a the former congressman and former presidential candidate Ron Paul, has been on “The Independents” more than once. But Pearl Jam — a k a Ron Paul’s son Rand, a one-term Republican senator who may well run for the presidency in 2016 — has yet to appear.

A few weeks after our conversation, I saw Kennedy onstage in a hotel ballroom, wearing purple spandex, gyrating to the soundtrack of “Flashdance” and hollering into a microphone, “Are you hungry for more liberty?” She was the M.C. for the Competitive Enterprise Institute’s annual dinner, which, as Welch put it to me, “in the tallest-dwarf category is considered to be one of D.C.'s best annual galas.” The C.E.I. is a 30-year-old organization that routinely sues federal agencies, often when new and onerous regulations are posted in the Federal Register. Tonight’s banquet had advertised itself as having an ‘80s theme, and so several of the 800 attendees arrived dressed as pop icons of that decade. After being introduced by Kennedy, the institute’s president, Lawson Bader, strode to the stage wearing the decidedly pre-1980s Scottish formal attire of black jacket and kilt. Announcing pending lawsuits against the Affordable Care Act and the N.S.A., Bader thundered, to righteous applause, “C.E.I. will continue to push back!”

Between dinner courses, Kennedy informed the audience that there was to be a contest, with a prize awarded to the attendee who had recently flouted the most egregious law or regulation. My tablemates — among them Welch; a longtime member of the libertarian Cato Institute; a French academic; and a woman dressed as Cyndi Lauper — each scribbled their infraction on a piece of paper. One had smoked a joint on the sidewalk with a stranger, while another had traveled to Cuba without authorization.

At the night’s conclusion, Kennedy announced the winner. It was a woman who, despite her lack of veterinary certification, had illegally massaged a pug.

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Kennedy, a former MTV personality and now a libertarian activist, performs at the annual dinner of the Competitive Enterprise Institute.CreditSarah & Samantha

Libertarians, who long have relished their role as acerbic sideline critics of American political theater, now find themselves and their movement thrust into the middle of it. For decades their ideas have had serious backing financially (most prominently by the Koch brothers, one of whom, David H., ran as vice president on the 1980 Libertarian Party ticket), intellectually (by way of policy shops like the Cato Institute and C.E.I.) and in the media (through platforms like Reason and, as of last year, “The Independents”). But today, for perhaps the first time, the libertarian movement appears to have genuine political momentum on its side. An estimated 54 percent of Americans now favor extending marriage rights to gay couples. Decriminalizing marijuana has become a mainstream position, while the drive to reduce sentences for minor drug offenders has led to the wondrous spectacle of Rick Perry — the governor of Texas, where more inmates are executed than in any other state — telling a Washington audience: “You want to talk about real conservative governance? Shut prisons down. Save that money.” The appetite for foreign intervention is at low ebb, with calls by Republicans to rein in federal profligacy now increasingly extending to the once-sacrosanct military budget. And deep concern over government surveillance looms as one of the few bipartisan sentiments in Washington, which is somewhat unanticipated given that the surveiller in chief, the former constitutional-law professor Barack Obama, had been described in a 2008 Times Op-Ed by the legal commentator Jeffrey Rosen as potentially “our first president who is a civil libertarian.”

Meanwhile, the age group most responsible for delivering Obama his two terms may well become a political wild card over time, in large part because of its libertarian leanings. Raised on the ad hoc communalism of the Internet, disenchanted by the Iraq War, reflexively tolerant of other lifestyles, appalled by government intrusion into their private affairs and increasingly convinced that the Obama economy is rigged against them, the millennials can no longer be regarded as faithful Democrats — and a recent poll confirmed that fully half of voters between ages 18 and 29 are unwedded to either party. Obama has profoundly disappointed many of these voters by shying away from marijuana decriminalization, by leading from behind on same-sex marriage, by trumping the Bush administration on illegal-immigrant deportations and by expanding Bush’s N.S.A. surveillance program. As one 30-year-old libertarian senior staff member on the Hill told me: “I think we expected this sort of thing from Bush. But Obama seemed to be hip and in touch with my generation, and then he goes and reads our emails.”

Early polls show young voters favoring Hillary Rodham Clinton in 2016, but their support could erode as they refamiliarize themselves with her, just as it did in 2008. Clinton has been even slower than Obama to embrace progressive social causes, while in foreign policy, she associates herself more with her former Senate colleague John McCain than with noninterventionists. Nor is Clinton likely to quell millennial fears about government surveillance. Welch says: “Hillary isn’t going to be any good on these issues. She has an authoritarian mind-set and has no interest in Edward Snowden, who’s a hero to a lot of these people.”

After eight years out of the White House, Republicans would seem well positioned to cast themselves as the fresh alternative, though perhaps only if the party first reappraises stances that young voters, in particular, regard as outdated. Emily Ekins, a pollster for the Reason Foundation, says: “Unlike with previous generations, we’re seeing a newer dimension emerge where they agree with Democrats on social issues, and on economic issues lean more to the right. It’s possible that Democrats will have to shift to the right on economic issues. But the Republicans will definitely have to move to the left on social issues. They just don’t have the numbers otherwise.” A G.O.P. more flexible on social issues might also appeal to another traditionally Democratic group with a libertarian tilt: the high-tech communities in Silicon Valley and elsewhere, whose mounting disdain for taxes, regulations and unions has become increasingly dissonant with their voting habits.

Hence the excitement about Rand Paul. It’s hardly surprising that Paul, in Ekins’s recent survey of millennial voters, came out ahead of all other potential Republican presidential candidates; on issues including same-sex marriage, surveillance and military intervention, his positions more closely mirror those of young voters than those of the G.O.P. establishment. Paul’s famous 13-hour filibuster last year, while ultimately failing to thwart the confirmation of the C.I.A. director John Brennan, lit afire the Twittersphere and compelled Republican leaders, who previously dismissed Paul as a fringe character, to add their own #StandWithRand endorsements. Paul has also gone to considerable lengths to court non-Republican audiences, like Berkeley students and the National Urban League. In a presidential field that could include Cruz, Jeb Bush, Marco Rubio, Chris Christie and Paul Ryan, Paul — who has called himself “libertarian-ish” — is by far the candidate most associated with the movement.

It’s nonetheless with some awkwardness that libertarians consider their sudden assimilation into the mainstream. Partisan gunslingers like Glenn Beck have recently called themselves libertarians, to the great annoyance of others in the movement. When I asked Kennedy if some of these new libertarians were former ideologues now rebranding themselves so as to broaden their appeal, she replied crisply, “Yes.” But she added that “the idea of having a really specific litmus test is ridiculous. It’s just another form of groupthink.” Still, even Rand Paul prompts notable skepticism among the die-hards. “When he talks about ‘Let’s stop nation-building and let’s start building bridges in Detroit,’ a lot of libertarians roll their eyes,” Welch told me. “But he’s done more to advance and popularize libertarian ideas in Washington than anyone else. In terms of changing the national debate, I think Rand has gone farther than his father.”

During the father’s two runs for president as a Republican, in 2008 and 2012, libertarian activists gave him momentum far beyond his popular appeal, packing caucus halls and organizing rallies. But it’s an open question whether these same activists will get off the sidelines and support his son, whose libertarian bona fides are less sure but whose chance of victory is far greater. And if they do, it’s unclear whether G.O.P. establishment figures can put aside their longtime distrust of libertarianism and welcome Paul’s bid to expand the party’s base. If this is indeed the libertarian moment, do either libertarians or Republicans intend to seize it?

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Senator Rand Paul has established himself as a national figure over the past 12 months, raising the question of whether he will campaign for the Republican nomination for president in 2016.Published OnJan. 25, 2014CreditCreditJabin Botsford for The New York Times

On the afternoon that I showed up to chat with the longtime libertarian writer and editor Nick Gillespie at the posh Washington offices of Reason, just off Dupont Circle, a dozen or so staff members were hanging out in the kitchen, drinking Green Hat gin. (It is named in honor of George Cassiday, a bootlegger who was known as “the man in the green hat” and who provided liquor to congressmen during Prohibition, thus making it a quintessentially libertarian beverage.) Gillespie poured me a glass and led me to a sitting area beside his office, which is festooned with vintage rock posters. Nick Gillespie is to libertarianism what Lou Reed is to rock ‘n’ roll, the quintessence of its outlaw spirit. He is 50, a former writer for teen and heavy-metal magazines, habitually garbed in black from head to toe, wry and mournful in expression, a tormented romantic who quotes Jack Kerouac. For the past 20 years, Gillespie has been a writer, editor and intellectual godfather for Reason, the movement’s leading journal since its founding in 1968 (and which today has a circulation of about 50,000, while its website receives 3.3 million visits a month). By the standards of libertarianism’s radical fringe, Gillespie is fairly tame: He prefers Federal Reserve currency over Bitcoin, has no personal interest in owning a semiautomatic weapon and faithfully votes in presidential elections, albeit for the Libertarian Party candidate.

His embrace of libertarianism coincided with a rejection of party ideology and collectivist thinking. As a graduate student during the 1980s and early 1990s at Temple and the State University of New York at Buffalo, Gillespie encountered the politically correct tunnel vision of what he calls “the professoriate,” which turned him away from liberalism for good. At the same time, Gillespie was unimpressed by Ronald Reagan, who declared a new “war on drugs,” raised the national drinking age to 21, raised all sorts of taxes, preserved Social Security which Gillespie regards as federally mandated generational theft) and in general claimed to champion American individualism while squashing it every chance he got.

“I was never conservative,” he told me as we sipped our gin. “Republicans always saw libertarians as nice to have around in case they wanted to score some weed, and we always knew where there was a party. And for a while it made sense to bunk up with them. But after a while, it would be like, ‘So if we agree on limited government, how about opening the borders?’ No, that’s crazy. ‘How about legalizing drugs? How about giving gays equal rights?’ No, come on, be serious. And so I thought, There’s nothing in this for me.”

Gillespie likes to point out that unlike the words “Democrat” and “Republican,” “libertarian” should be seen as a modifier rather than a noun — an attitude, not a fixed object. A cynic might assert that this is exactly the kind of semantic cop-out that relegates Gillespie’s too-cool-for-school sect to the margins. Not surprisingly, he begged to differ. “It’s wedded to an epistemological humility,” he told me, “that proceeds from the assumption that we don’t know as much as we think we do, and so you have to be really cautious about policies that seek to completely reshape the world. It’s better to run trials and experiments, as John Stuart Mill talked about. The whole point of America — and this is an admixture of Saul Bellow and Heidegger and Jim Morrison lyrics — is that it’s in a constant state of becoming, constantly changing and mongrelizing. We’re doing exactly what free minds and free markets allow you to do. Part of why I’m a libertarian is that if you restrict people less, interesting stuff happens.”

Continuing his riff with beatnik locomotion, he added: “It’s like what happens in garages. Rock bands form in garages. Computer companies. And O.K., occasionally serial murders. But as long as you’re not just parking your car there, garages are always interesting.”

Gillespie, Kennedy and virtually every other libertarian leader I met told me that their philosophy was unique for its “consistency.” And yet determining what it consistently looks like in practice can be a frustrating exercise. Foreign policy is the easiest place to start. With rare exceptions, libertarian leaders have recently advocated staying out of Libya, Syria, Iran, Iraq and Nigeria. Informing their reluctance to intervene overseas is the recent experience of post-9/11 neoconservatism. Gillespie, smirking, told me: “Sarah Palin doesn’t deserve credit for anything, but she wasn’t the only one who didn’t understand what the Bush Doctrine meant. And Obama’s been as bad as Bush, but with less of an excuse. We don’t have to pretend anymore that radical Islam is an existential threat to the West. It’s herpes, but it’s not AIDS. It’s a chronic condition, but it won’t kill us. Just keep the attacks to a minimum.” Gillespie and others maintain that theirs is a posture of restraint, not isolationism. But it’s an impulse reminiscent of Ron Paul, who not only opposed both Iraq wars but has also stated that President Lincoln was imprudent in declaring war on the South. Ben Domenech, whose web magazine, The Federalist, frequently publishes commentators from the movement, said, “Libertarians have not yet espoused a comprehensive view of the world that shares more in common with, say, Bob Gates’s realism than it does with isolationism.”

Beyond avoiding adventurism overseas, defining the libertarian agenda gets even trickier. Virtually all libertarians enthusiastically favor marijuana legalization, but they become more subdued when the subject turns to cocaine and heroin. They are united against most benefit programs but divided on whether to champion the outright abolition of Social Security, Medicare and Medicaid. On immigration policy, the purist stance would call for completely open borders, which Gillespie and a few others in the movement advocate, though not quite literally, and so down the slippery slope the ideal skids, into a murky world of armed deportation agents and registration systems and random drug testing. (Libertarian-leaning elected officials often say that there can be no open borders as long as the welfare state exists for immigrants to drain. Gillespie is among those who consider this a dodge.)

The so-called cultural issues have traditionally been a safe haven of libertarian concurrence and, as well, a showcase for the movement to demonstrate how it would apply laissez-faire principles to personal freedoms. One of the more pugnacious advocates of this across-the-board approach is Cathy Reisenwitz, a 28-year-old Washington-based journalist who has a tattoo under her right biceps that reads, “I Own Me.” (“What does that mean, ‘I own myself?’ ” David Frum, a former speechwriter for George W. Bush and Republican commentator, sputtered in exasperation when we spoke later. “Can I sell myself? If I can’t, I don’t own myself.”) Reisenwitz, a former staff member at Reason, writes a blog called Sex and the State that, she told me, “thoroughly disassociates culture wars from free markets — I disavow them 100 percent.” When I asked her where she stood on abortion, Reisenwitz replied, “I do not support any legislative restrictions on health care.” She also espoused purity on same-sex marriage, telling me, “If you’re going to say, ‘Government should be out of marriage,’ and you’re creating petitions and submitting bills, awesome. But in the meantime, if government is going to be involved in marriage as an institution, it should be available for everyone.”

But libertarian consistency on even these social issues is in the eye of the beholder. In 1968 Ayn Rand flatly declared: “An embryo has no rights. . . . Abortion is a moral right.” Twenty years later, however, the Libertarian Party proffered as its presidential candidate Ron Paul, an OB-GYN who has argued that the movement’s bedrock nonaggression principle should apply above all to the most defenseless, the unborn. Today one of the more fluent anti-abortion journalists is also a self-identified libertarian: Mollie Z. Hemingway, senior editor at The Federalist, differs significantly from Reisenwitz on the subject of marriage, on the basis of what Hemingway maintains are libertarian grounds.

Even acceptance of same-sex marriage, an ostensibly pro-freedom position that has become nearly nonnegotiable for younger voters, is a stance that some self-described libertarians will not sign onto. When I asked Hemingway what she thought of extending rights to gay couples, she replied carefully: “Well, I have always thought that government should be so small that it doesn’t have a role in giving benefits. It’s interesting to me that libertarians see government redefining the institution as something that will maximize liberty. And I am very skeptical about that.” She added that while “people should be free to organize their own lifestyle,” the state had a unique interest in protecting heterosexual marriage, because it was “the relationship that’s ordered to producing children.”

This was a familiar point — but for social conservatives like Rick Santorum, not for libertarians. When I pressed her on it, Hemingway said: “Do I think the state should change the definition of marriage to allow same-sex couples? I think people should be free to organize their own lives however they wish. I’m skeptical about the way we’re accomplishing this. I don’t know. I feel like I need to think about it more.”

This is not the first moment that libertarians have claimed as their own. In 1971, The New York Times Magazine published on its cover a 5,200-word article by two young authors (one of them was Louis Rossetto Jr., later a founding publisher of Wired) who pronounced libertarianism “undoubtedly the fastest-growing movement in the country.” That same year, the Libertarian Party was formed; a year later, its 1972 presidential ticket of the philosophy professor John Hospers and the TV talk-show host Tonie Nathan received one electoral vote. Forty years later, little had changed. The Libertarian Party’s 2012 candidate, Gary Johnson, a former governor of New Mexico, spent a million dollars and received more than a million votes — a better showing than any of his party’s predecessors, but not good enough to even remotely sway either the presidential election or the terms of the national debate.

Why has the libertarian takeover not come to pass? With charming understatement, the authors of the 1971 magazine article pointed out a small complication to this otherwise-unstoppable tidal wave they predicted. “At present,” they wrote, “the only areas of disagreement within the libertarian movement are whether the movement should strive for anarchy or for limited government, and whether it should work through revolution or within the system.” That tension has not gone away. During my travels with libertarians, I met many who cheerfully identified themselves to me as “anarcho-capitalists,” and I sat in on one speech — by Bill Buppert, a blogger and the author of a book called “ZeroGov” — that featured applause lines like “any tax rate above zero percent is immoral” and “there are no good cops out there.” I also encountered Beltway libertarians who revolt at the ballot box, like Gene Healy, a Cato Institute vice president, who told me, “Usually I just vote for whoever the Libertarian Party throws up, even if it’s a guy living in his car.”

Even if libertarians willingly engage the political process, there’s little to guarantee that the process will engage them back. Each party would be only too happy to receive the libertarian vote as long as it doesn’t have to do much of anything to earn it. But not since the days of the Vietnam War and Nixon’s imperial presidency have libertarians seen much profit in an alliance with the big-government Democrats. Instead, ever since a newly inaugurated President Reagan declared, “Government is the problem,” politically practical libertarians have been more apt to cast their lot with the G.O.P.

And yet, the relationship between the libertarian movement and the Republican Party is a fraught one, to say the least. The G.O.P.'s traditional “three-legged stool” is propped up by not only libertarian advocates of free markets but also by hawks, who believe in a well-financed and forward-leaning military, and by social conservatives, who believe that the government should play a role in preserving family values. Neither of the other legs feels supported by libertarians, and with cause. It’s hard to know whether Republicans in one or both of these other camps can ever make peace with a movement that they have spent a generation deriding. In a 1997 Weekly Standard article titled “The Libertarian Temptation,” David Frum belittled its followers as feckless hedonists who “claim that snorting cocaine is some sort of fundamental human right.” When I recently asked Frum if his feelings toward libertarianism had mellowed, he assured me that they had not.

“It’s a completely closed and airless ideological system that doesn’t respond well to reality,” he said. “Libertarians are like Marxists in that they have prophets like von Mises and Hayek, and they quote from their holy scripture, and they don’t have to engage.”

In practice, whenever a Republican politician has behaved more like a libertarian than a party loyalist, the party has made him pay for it. Despite the fact that Ron Paul served nearly two decades in the House and established seniority on the Financial Services Committee, in late 2010 the incoming speaker, John Boehner, reportedly sought to deny Paul a subcommittee chairmanship (owing to Paul’s views on monetary policy) before eventually buckling to the outcries of Paul supporters. On the House floor, Paul typically sat with a fellow outcast, the antiwar Republican Walter Jones. During the G.O.P. presidential primaries of 2008 and 2012, the other candidates treated him with amused derision.

Since Paul vacated the Capitol, the libertarian movement’s latest Republican congressional hero has been Justin Amash, a 34-year-old Arab-American and two-term House member from Grand Rapids, Mich., whose office wall sports adjoining posters of Ayn Rand and Mickey Mouse. Amash is the founder of the House Liberty Caucus, consisting of about 30 libertarian-inclined Republicans (and occasional Democratic visitors like Jared Polis). The caucus serves as a de facto competitor to the House’s conservative think tank, the Republican Study Committee, which Amash considers suspect in part because of its support for big military budgets. Even by the standards of his 2010 Tea Party class, G.O.P. leaders have viewed Amash as the antithesis of a team player for voting against Republican budgets that in his view did not cut deeply enough and for siding with liberal Democrats to end the war in Afghanistan. Last year Amash horrified military hawks and the intelligence community by introducing an amendment to defund the N.S.A.'s domestic phone-surveillance program, which came within a dozen votes of passage. Having already stripped the video-game-obsessed congressman of his seat on the Budget Committee, senior Republicans have now invested heavily in Amash’s primary opponent in hopes of vaporizing his presence in Congress altogether.

One afternoon in late May, I had lunch in Chinatown with Amash, just a couple of hours after House Republican leaders gutted another of his anti-N.S.A. bills. He nonetheless wore a defiant smile. The public was on his side, Amash said, and not just Republicans — and for precisely this reason, he added, G.O.P. leaders “view us as a threat to the established order.”

Still, the anti-abortion and border-security-advocating Amash is hardly a radical libertarian. For the most part, his views are inseparable from those of Rand Paul. And so I asked him, “Given how leaders in your party have reacted to your legislative proposals, how do you think they’re going to react if Paul runs for president?”

“I believe very strongly that he could be the nominee,” Amash said. “He just needs to get his message out there and push back against the caricature that some of the political establishment will make of Senator Paul. They’re doing it because they’re afraid of him.”

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Senator Rand Paul, at the National Urban League convention, speaks with Laysha Ward, an executive at Target.CreditMark Peterson/Redux, for The New York Times

“Why?”

Because, Amash said, Paul shared his ability to appeal to all kinds of people, not just big donors and not just entrenched Republicans. “He destroys their system,” he said with a thin smile.

“I think the war on drugs has had a disproportionate racial outcome,” Rand Paul said as he stood in his cowboy boots before a small gathering of Rotary Club members in Shelbyville, Ky. “Three out of four people in prison are black or brown. White people do drugs too, but either they don’t get caught or they have better attorneys or they don’t live in poverty. It’s an inadvertent outcome, and we ought to do something about it. As a Christian, I believe in redemption. I believe in a second chance. I think drugs are bad. I think even marijuana is deleterious. However, a 20-year-old kid who does make this mistake ought to get his right to vote back, ought not to be locked up in jail for 10 or 15 years.”

It was not the kind of message that a Republican presidential aspirant typically delivers to an all-white audience. But as he continued with his off-the-cuff remarks, I began to see what the Kentucky senator was up to. After observing, “We’re a pro-coal state, and I’m a pro-coal senator,” Paul then told the attendees, “but I’m not for no regulations on coal,” even going so far as to suggest that today’s environment was better than a century ago “and some of that’s through government regulation.” He assured the audience that he was all for affordable health care, just not the Affordable Care Act — “it’s really about freedom versus coercion.” And as his bedrock economic principle, Paul said, “We can grow as a country, but government needs to be minimized and the private market needs to be maximized.” But he was careful to say, “That doesn’t mean no government.”

Despite Amash’s claim that Paul “destroys their system,” nothing about his rhetoric sounded remotely worrisome to the Republican establishment. At the same time, the political artfulness of his oratory was hard to miss. Rand Paul was road-testing a kinder, gentler libertarianism to a mass market — in effect triangulating (to use the term associated with Bill Clinton, whose moral lapses Paul frequently cites) Republicans, Democrats and libertarians. It is a maneuver that, if successful, could amount to a considerable triumph for the movement. By calling for significantly reduced sentences for drug offenders, Paul has slyly redefined the terms of the marijuana debate with a libertarian tilt. Though a self-proclaimed “traditionalist” on marriage, his seeming contentment with judicial trends on the subject is far more in keeping with Democrats than with others in the G.O.P. presidential field. And if Paul’s foreign-policy addresses have more in common with the realism espoused by Robert Gates, a former defense secretary, than with his father’s laissez-faire approach to the outside world, his worldview nonetheless marks a clear break from the hawkishness that still predominates within the Republican Party.

The hawks have taken notice. Dick Cheney dusted off the word “isolationism” — which, in foreign-policy-speak, is essentially a synonym for “wild-eyed extremism” — in describing Paul’s aversion to a renewed military presence in Iraq. Rick Perry made a similar charge in a Washington Post op-ed titled, “Why Rand Paul Is Wrong on Iraq.” Senator John McCain has been particularly caustic, saying that a Rand Paul foreign policy would constitute a dangerous retreat into a “fortress America” and dismissing Paul’s drone filibuster as a stunt intended to “fire up impressionable libertarian kids in college dorms.” Paul, in turn, has enthusiastically ripped into each denouncer.

“I think that Senator Paul has been very clever in trying to couch his foreign policy in terms that would appeal to most Republicans,” said the conservative writer Ramesh Ponnuru, who, like David Frum, has qualms about the libertarian movement. “But at the end of the day, he’s a hard-core anti-interventionist, and Republican voters aren’t.” Ponnuru’s latter assertion will be tested in the 2016 primaries, which could include, in descending order of hawkishness, Rubio, Perry, Cruz and then Paul (with foreign-policy stances by Christie, Bush and others yet to be articulated).

Over the past year, Paul has drawn a great deal of attention as the only likely Republican presidential candidate to venture into the hostile territory of college campuses and Latino and African-American groups. (Following the Rotary Club talk in Shelbyville, I watched Paul dedicate a plaque to the memory of an African-American doctor and civil rights activist. An 89-year-old black woman named Frances Marshall looked on with pronounced skepticism, telling me, “Actions speak louder than words.”)

Less noticed is how Paul has taken pains to mollify the Republican base. He reminds audiences like the one in Shelbyville that he is “pro-life.” His assaults on the Affordable Care Act are frequent. Faced with criticisms that he is anti-Israel, Paul three months ago introduced a bill he called the Stand With Israel Act, in which the Palestinian government would not receive any further foreign aid unless it recognized Israel as a state. (“It was complete pandering,” the libertarian Hill staff member told me.) Still, the vitriol aimed at Paul by McCain, Cheney and others in his party defies Reagan’s 11th Commandment — “Thou shalt not speak ill of thy fellow Republican” — and harks back to the enduring animus between hawks and libertarians.

I asked Reince Priebus, the chairman of the Republican National Committee, what he made of this rift. “I think most people share my view about Rand as being pure-hearted in his views and intentions,” he replied diplomatically. “I just think he has some different opinions that not everyone shares. There’s going to be disagreements within our party. Look at how the Democrats are lambasting the president over his pathetic approach to the border. Look, if Rand Paul was such an outsider, I wouldn’t have him speaking at three of our national events. I see Rand Paul as someone who will build a lot of bridges in our party. Last year, he and I did a listening session with libertarians in New Hampshire. Libertarianism is certainly growing in the country, and I think it’s an opportunity for the Republican Party to grow as well. And I see our party as being very welcoming to the libertarian movement and to Rand Paul. That doesn’t mean you won’t have disputes.”

Last month I dropped by the Russell Senate Office Building to talk to Paul about his libertarian-Republican tightrope walk. Paul, 51 and a native Texan, possesses a supple mind and is a preternaturally confident speaker for someone who has held office for only four years. At the same time, Paul is not particularly enthusiastic about the glad-handing niceties that come with the job. “Good to see you,” he mumbled, then flopped down into a chair in his office’s conference room and fixed me with an impatient stare. I got to the point. Were we living in a libertarian “moment,” or was that wishful thinking on the part of Nick Gillespie and others?

“I think a plurality of Americans don’t consider themselves to be either Republicans or Democrats,” Paul said, citing young people and Silicon Valley entrepreneurs in particular. “I also think there was a time, maybe 30 years ago, when ‘libertarian’ was a term that scared people. Now I think it seems more like a moderate point of view. So I think the term is something that is definitely attracting, not repelling people.”

Paul qualified that observation by noting that the word itself encompassed a spectrum of positions. “What I try to point out when people say, ‘Oh, you’re an isolationist,’ I say, ‘No, there’s two poles: One is that we’re nowhere any of the time, the other is we’re everywhere all the time.’ Right now we’re much closer to the latter extreme pole — and that’s also coming from my party, the neoconservatives. So, really, libertarianism might be more like foreign-policy realism. There may be some libertarians who say, ‘By golly, we’re not going anywhere unless they attack us.’ I think I consider myself to be more moderate on the foreign-policy spectrum.”

“Do you think some political forces in Washington, like big defense contractors, hear your views on the defense budget and regard you as an existential threat?” I asked.

“I don’t think you should ever make a decision on what weapons systems we use based on the bottom line of those who make the weapons systems,” he said. “That makes some people fearful.” Grinning, he added, “But it should make other people feel hopeful.”

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Participants at PorcFest, an annual libertarian festival held in New Hampshire in June. (It derives its name from the porcupine.)CreditTennyson McCalla

During our conversation, Paul made a point of characterizing libertarianism as being “moderate” rather than liberal on social issues. Movement leaders would likely object, but Paul’s preoccupation is with swaying the center-right.

“The party can’t become the opposite of what it is,” he told me. “If you tell people from Alabama, Mississippi or Georgia, ‘You know what, guys, we’ve been wrong, and we’re gonna be the pro-gay-marriage party,’ they’re either gonna stay home or — I mean, many of these people joined the Republican Party because of these social issues. So I don’t think we can completely flip. But can we become, to use the overused term, a bigger tent? I think we can and can agree to disagree on a lot of these issues. I think the party will evolve. It’ll either continue to lose, or it’ll become a bigger place where there’s a mixture of opinions.”

In effect, Paul was saying that the way for Republicans to win was to become more libertarian — though only up to a point. Purity was the movement’s game, not his. Paul reminded me that he worked on his father’s 1988 Libertarian Party presidential campaign and felt a great deal of sympathy for anyone trying to take on the major parties. “I also gathered signatures to get him on the ballot,” he said. “I know what a thankless job that is. Anybody who stands in a parking lot is thought to be an extremist.”

But later, with an irritated edge to his voice, Paul added: “Some people are purists, and I get grief all the time — all these libertarian websites hating on me because I’m not as pure as my dad. And I’m putting restrictions on foreign aid instead of eliminating foreign aid altogether. And I’m like: ‘Look, guys, I’m having trouble putting these restrictions on, much less eliminating them! So give me a break!’ ”

This June I watched Nick Gillespie deliver the keynote address at PorcFest, the annual libertarian outdoor festival held in Lancaster, N.H., and named for the area’s ubiquitous porcupine. About 500 campers sat attentively, while several others stood off to the side, Hula-Hooping as they listened. Arrayed before Gillespie were several boxes of exotically flavored Pop-Tarts that he had purchased at the Lancaster grocery store. He held them up as evidence that individualism was flourishing and choices were in abundance or, as he put it, “The libertarian moment is now.” Their moment had arrived, Gillespie said, “because the main political drivers have destroyed their credibility. Only the dead think the G.O.P. is the party of small government.” At the same time, he added, “the Democrats had a clean shot to demonstrate that they’d protect our liberties, and they proved themselves to be utter frauds.”

With deadpan aplomb, Gillespie then said, “If we can have 20 different types of Pop-Tarts, maybe we can have more than two types of political identification.”

After the speech was over and Gillespie gamely posed for a few pictures with admirers, I cornered him and asked him if he was suggesting that libertarians leave the G.O.P.-flavored Pop-Tarts on the shelf. Gillespie said it all depended on Republicans. “This is the fundamental question for the Republican Party,” he said. “Are they going to embrace the libertarian elements of Rand Paul and Justin Amash? Because that’s their only way out. They’re at 25 percent self-identification, and it’s not going to climb back up if they keep re-electing the old horses. Libertarians don’t need them. We’re already alienated and out of the mainstream. We don’t need the Republican Party in the way that they need the energy and the vision of libertarians.”

But, I wanted to know, would libertarians be willing to meet the G.O.P. somewhere in the middle? Among the 1,700 or so attendees, I had seen guns and Bitcoins and slogans like “Liberty: Too Big to Fail” and “I Do Not Consent to Searches.” What I had not seen or heard was any show of support for Rand Paul. The crowd here at PorcFest, many of them young, all of them passionate, represented just the sort of army that Paul would need in the early primary states and beyond — the same sort of army, in fact, that powered his father’s improbable showing in previous elections. But they still talked more about the father than the son.

Gillespie acknowledged that the answer remained unclear. “I think that if a major-party candidate articulates 75 percent of the catechism,” he said, “both self-identified libertarians and people who don’t realize they’re libertarians would vote for him.” But then again, he said, it might take “a hundred years or something” for his movement to find its true expression in a political party. “We’ve gone from a movement that didn’t exist, then we all believe in this roughly similar thing, then we have a dalliance with the G.O.P., then we realize, no, we’re totally separate. And then we find out, no, we really need to activate politically in a conventional two-party system,” he said, his tone betraying little concern for the pace of this process. “And it may be we’re still some years away from that. I don’t know.”

Our libertarian moment, in other words, might very well pass unexploited. But it remained, for Gillespie and his fellow travelers, a moment to savor: Pop-Tarts washed down with Green Hat gin. Interesting stuff was happening in the garage called America, and you could try to change the system, or you could also elect to be boring. Either way, you were at perfect liberty.